Trying to solve the Poschl-Teller potential (quantum mechanics) 1. The problem statement, all variables and given/known data I have a superpotential that give me 2 of the Poschl-Teller potentials. The superpotential is: W(x)=-b*cot(x) The Poschl-Teller potentials are: J(x,b)=b(b-1)/(sin(x))^2-b^2 K(x,b)=b(b+1)/(sin(x))^2-b^2 2. Relevant equations Schrodinger equation: Hψ=Eψ 3. The attempt at a solution I placed the potential in Schrodinger equation (neglecting the existence of constants) and received the following equations: ψ''(x)+(2E-J)ψ(x)=0 ψ''(x)+(2E-K)ψ(x)=0 I do not know what the next step I should do I know I need to get to Legendre polynomial but I don't know how... Can anyone show me how to do it?